Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 478 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹96 (d) ₹48
2. 2.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹81 (c) ₹27 (d) ₹55
3. 3.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
4. 4.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹168 (b) ₹210 (c) ₹126 (d) ₹42
5. 5.If 5 pens cost ₹105, how much do 12 pens cost? (a) ₹252 (b) ₹1260 (c) ₹112 (d) ₹273
6. 6.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹90 (d) ₹60
7. 7.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 9 days
8. 8.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 4 days (d) 36 days
9. 9.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 17 days (d) 22 days
10. 10.If 9 kites cost ₹36, how much do 10 kites cost? (a) ₹44 (b) ₹360 (c) ₹37 (d) ₹40
11. 11.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 1 day (d) 7 days
12. 12.If 4 notebooks cost ₹68, how much do 11 notebooks cost? (a) ₹748 (b) ₹75 (c) ₹204 (d) ₹187
13. 13.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹31 (d) ₹124
14. 14.If 9 notebooks cost ₹162, how much do 7 notebooks cost? (a) ₹160 (b) ₹1134 (c) ₹126 (d) ₹144
15. 15.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹90 (b) ₹75 (c) ₹15 (d) ₹105
16. 16.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 57 days (c) 56 days (d) 8 days
17. 17.If 2 mangoes cost ₹8, how much do 3 mangoes cost? (a) ₹9 (b) ₹24 (c) ₹16 (d) ₹12
18. 18.If 6 kites cost ₹42, how much do 11 kites cost? (a) ₹77 (b) ₹462 (c) ₹47 (d) ₹84
19. 19.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹115 (b) ₹46 (c) ₹230 (d) ₹184
20. 20.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹164 (d) ₹287
21. 21.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹30 (d) ₹45
22. 22.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 13 days (d) 1 day
23. 23.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 16 days (d) 11 days
24. 24.If 8 kites cost ₹168, how much do 10 kites cost? (a) ₹1680 (b) ₹170 (c) ₹231 (d) ₹210
25. 25.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹99 (b) ₹132 (c) ₹33 (d) ₹66
26. 26.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 22 days (d) 21 days
27. 27.If 3 kites cost ₹66, how much do 8 kites cost? (a) ₹71 (b) ₹198 (c) ₹528 (d) ₹176
28. 28.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹36 (d) ₹63
29. 29.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
30. 30.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 6 days (d) 7 days
31. 31.If 2 kites cost ₹42, how much do 6 kites cost? (a) ₹252 (b) ₹147 (c) ₹46 (d) ₹126
32. 32.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹68 (d) ₹51
33. 33.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹165 (d) ₹99
34. 34.If 2 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹38 (b) ₹150 (c) ₹165 (d) ₹300
35. 35.If 9 kites cost ₹171, how much do 4 kites cost? (a) ₹76 (b) ₹684 (c) ₹166 (d) ₹95
36. 36.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹6 (b) ₹21 (c) ₹12 (d) ₹30
37. 37.If 6 notebooks cost ₹132, how much do 7 notebooks cost? (a) ₹176 (b) ₹924 (c) ₹133 (d) ₹154
38. 38.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 43 days (d) 42 days
39. 39.If 6 pens cost ₹126, how much do 12 pens cost? (a) ₹132 (b) ₹1512 (c) ₹273 (d) ₹252
40. 40.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹24 (b) ₹8 (c) ₹40 (d) ₹56

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